Two dimensional (2D) materials with interesting fundamental physics and potential applications attract tremendous efforts to study. The versatile properties of 2D materials can be further tailored by tuning the electronic structure with the layer-stacking arrangement, of which the main adjustable parameters include the thickness and the in-plane twist angle between layers. The Angle-Resolved Photoemission Spectroscopy (ARPES) has become a canonical tool to study the electronic structure of crystalline materials. The recent development of ARPES with sub-micrometre spatial resolution (micro-ARPES) has made it possible to study the electronic structure of materials with mesoscopic domains. In this thesis, we use micro-ARPES to investigate the spatially-resolved electronic structure of a series of few-layer materials: 1. We explore the electronic structure of the domains with different number of layers in few-layer graphene on copper substrate. We observe a layer- dependent substrate doping effect in which the Fermi surface of graphene shifts with the increase of number of layers, which is then explained by a multilayer effective capacitor model. 2. We systematically study the twist angle evolution of the energy band of twisted few-layer graphene over a wide range of twist angles (from 5° to 31°). We directly observe van Hove Singularities (vHSs) in twisted bilayer graphene with wide tunable energy range over 2 eV. In addition, the formation of multiple vHSs (at different binding energies) is observed in trilayer graphene. The large tuning range of vHS binding energy in twisted few-layer graphene provides a promising material base for optoelectrical applications with broad-band wavelength selectivity. 3. To better extract the energy band features from ARPES data, we propose a new method with a convolutional neural network (CNN) that achieves comparable or better results than traditional derivative based methods. Besides ARPES study, this thesis also includes the study of surface reconstruction for the layered material Bi2O2Se with the analysis of Scanning Tunnelling Microscopy (STM) images. To explain the origin of the pattern, we propose a tile model that produces the identical statistics with the experiment.

A major area of interest in condensed matter physics over the past decades has been the emergence of new states of matter from strongly correlated electron systems. A few limited examples would be the emergence of unconventional superconductivity in the high-T$_c$ superconductors and heavy-fermion systems, the appearance of the skyrmion magnetic vortex state in MnSi and magnetically mediated superconductivity in UGe$_2$. While detailed studies of many of the emergent phases have been made, there are still many gaps in understanding of the underlying states and mechanisms that allow them to form. This work aims to add to knowledge of the basic physics behind such states, and the changes within them as they are tuned to approach new phases. The cubic perovskite material SrTiO$_3$ has been studied for many decades and is well-documented to be an incipient ferroelectric, theorised to exist in the absence of any tuning in the proximity of a ferroelectric quantum critical point. This work presents the first high-precision dielectric measurements under hydrostatic pressure carried out on a quantum critical ferroelectric, leading to a full pressure-temperature phase diagram for SrTiO$_3$. The influence of quantum critical fluctuations is seen to diminish as the system is tuned away from the quantum critical point and a novel low temperature phase is shown to be emergent from it. The Néel Temperature of the two-dimensional antiferromagnet FePS$_3$ was found to increase linearly with applied hydrostatic pressure. Evidence of an insulator-metal transition is also presented, and an unexplained upturn in the resistivity at low temperatures in the metallic phase.

This thesis covers my work in the field of closed, repeatedly driven, Hamiltonian systems. These systems do not exchange particles with the surrounding environment and their time-evolution is described by Hamilton's equations of motion (in the classical framework) or the Schroedinger equation (in the quantum framework). Their interaction with the environment is encoded into the time-dependence of the system's Hamiltonian. Chapter 1 is an "Overview" in which the status of the field, my contributions and future prospective are outlined. Chapters 2 to 4 provide the theoretical background which is used in Chapters 5 to 7 to derive some original results. These results show that in Hamiltonian systems, after many driving events, universal properties emerge. In particular, using the framework of the linear Boltzmann equation, I have studied the dynamics of a mobile, light impurity in a gas of heavy particles. The impurity's kinetic energy increases and, in the long time limit, approaches a non-thermal asymptotic distribution. The significance of this work is to show explicitly the emergence of a non-thermal distribution in a closed, driven system. Moreover, using the work-fluctuation theorems, I have studied the character of the energy distribution of a generic isolated system driven according a generic protocol. Both thermal and non-thermal distributions can be realized for the same system by changing the characteristics of the driving protocol. These two different regimes are separated by a dynamical phase transition. Finally, I have used the Floquet Theory and the Magnus Expansion to analyze the behavior of a generic interacting system which is driven periodically in time. For fast driving the system is unable to absorb energy and remains localized in the low energy part of the Hilbert space while for slow driving the system absorbs energy and, in the long time limit, it is delocalized in the entire Hilbert space. These two qualitatively different behaviors are separated by a many-body localization transition which is related to the break down of the Magnus expansion at the critical value of the driving frequency.

<div>The quantum phase transitions and exotic excitations are exciting and important topics of nowadays condensed matter theory. Topologically protected excitations are of great interest for potential applications in quantum computing. This Thesis explores two examples of exotic topologically protected excitations, Majorana fermions and parafermions in hybrid superconductor/semiconductor systems.</div><div><br></div><div>In the first part of the thesis, after a brief review of ideas on Majorana zero modes in solid state systems obtained by researchers over the past decade, I present our study of the emergence of Majorana fermions in charge carrier holes doped quantum wires. Study of Majorana modes in this system requires understanding Luttinger holes in low dimensions, which is also crucial for numerous spin-dependent phenomena, emerging field of spintronics and nanotechnology. We find that hole-doped quantum wires that are proximity coupled to a conventional s-wave superconductor is a promising system for the observation of Majorana fermions. We advanced understanding of Luttinger holes in quantum wells and quantum wires. We have shown that the vast majority of earlier treatments of Luttinger holes ignored an important effect, a mutual transformation of heavy and light holes at the heteroboundaries. We have derived the effective hole Hamiltonians in the ground size-quantized sub-bands of quantum wells and quantum wires. The effect of mutual transformation of holes is crucial for understanding Zeeman and spin-orbit coupling, and results in several spin-orbit terms linear in momentum in hole-doped quantum wires. We discuss the criterion for realizing Majorana modes in charge carrier hole systems and show that GaAs or InSb hole wires shall exhibit stronger topological superconducting pairing, providing additional opportunities for its control compared to intensively studies InSb and InAs electron systems.</div><div><br></div><div>In the second part of the thesis, I first introduce the basic facts of the current theoretical understanding of the fractional quantum Hall effect and a theoretical model of parafermion excitations. Parafermion zero modes are promising for universal quantum computing. However, physical systems that are predicted to host these exotic excitations are rare and difficult to realize in experiments. I present our work on modeling domain walls on the boundary between gate-induced polarized and unpolarized domains of the fractional quantum Hall effect system near the spin transitions, and the emergence of the parafermion zero modes when such domain wall is proximity coupled to an s-wave superconductor. Exact diagonalization of the Hamiltonian in a disk and torus geometries proves formation of the counter-propagating edge states with different spin polarizations at the boundaries between areas of the electron liquid in polarized and unpolarized filling factor $\nu=2/3$ phases. By analytical and numerical methods we find the conditions for emergence of parafermion zero modes in hybrid fractional quantum Hall/s-wave superconductor system. The phase diagram indicates that the parafermionic phase, which is represented by the six-fold ground state degeneracy, is separated from other phases by a topological phase transition. Such parafermion modes are experimentally feasible. They present a vital step toward the realization of Fibonacci anyons that allow a full universal set of quantum operations with topologically protected quasiparticles.</div><div><br></div>

Recent experimental and theoretical studies have found evidence of coupled interactions between magnons and phonons. The aim of this study is to construct a model of coupled magnons and phonons, as well as analysing their frequency spectrum. The model is derived by quantizing spin and lattice degrees of freedom, and the frequency spectrum is derived by solving the equations of motion. We found that both the strength and the composition of the coupled interactions affect the frequencies of magnons and phonons, with emphasis on the magnons. Their frequencies are imaginary close to the center of the Brillouin zone, which opens questions for future research.

O modelo de Heisenberg destaca-se no estudo do magnetismo com origem em momentos magnéticos localizados. Semelhante ao bem conhecido modelo clássico de Ising, ele incorpora, no entanto, flutuações quânticas. Estamos interessados em sistemas antiferromagnéticos descritos pelo Hamiltoniano de Heisenberg com anisotropia de troca e que, eventualmente, possam apresentar magnetizações não-nulas. Neste trabalho, lidamos com sistemas não-homogêneos, apresentando impurezas e/ou sujeitos a condições de contorno abertas. Para tanto, utilizamos a Teoria do Funcional da Densidade, que proporciona uma metodologia de obtenção de resultados para um sistema não-homogêneo a partir dos resultados conhecidos do mesmo sistema quando homogêneo. Nosso trabalho resume-se a duas partes. Na primeira parte, trabalhamos inicialmente com um funcional, na aproximação ``local para o spin\'\'(LSA), advindo da Teoria de Ondas de Spin, válido para anisotropia de troca com simetria XXZ e magnetização do sistema nula. E na segunda, exploramos a possibilidade de construção de um funcional, na aproximação LSA, válido para anisotropia de troca mas com um adicional: válido para magnetizações não-nulas. Os resultados advindos dos funcionais são confrontados com resultados numericamente exatos obtidos de um programa em Fortran 90, que diagonaliza cadeias de spins na presença ou não de impurezas, para qualquer condição de contorno, descritas pelo modelo de Heisenberg com anisotropia de troca. / The Heisenberg Model is generally recognized in the study of electromagnetism with origin in localized magnetic moments. Similar to the well known classical Ising model, it incorporates, however, quantum flutuations. We are interested in antiferromagnetic systems described by the Heisenberg Hamiltonian with exchange anisotropy and, eventually, non-null magnetizations. In this work, we deal with non-homogeneous systems with impurities. For this, we use Density Functional Theory and the Local Spin Aproximation (LSA), which provide a methodology for obtaining results of a non-homogeneous system from known results of the same but homogeneous system. Initially, we work with a functional provided by Spin Wave Theory on the LSA approximation, valid for anisotropies with XXZ simmetry and null magnetization. After that, we deal with the possibility of building a functional on LSA approximation valid also for exchange anisotropy but with an additional: applicable for non-null magnetizations.

Um estudo experimental sobre os aspectos estruturais e dinâmicos de um complexo hidratado de fragmentos de DNA (150 pb) e fases lamelares de lipídios zwitteriônicos é apresentado. Variando-se a hidratação, é possível controlar o confinamento imposto por essa matriz hospedeira sobre os nucleotídeos inseridos na camada aquosa. O arranjo supramolecular do complexo é investigado por difração de raios X e técnicas de microscopia óptica e eletrônica. Um rico polimorfismo de mesofases é observado em função do confinamento. No regime mais hidratado, os fragmentos se distribuem segundo uma orientação nemática entre as membranas. À medida que a quantidade de água diminui, o confinamento das bicamadas sobre os nucleotídeos aumenta e correlações transmembranares aparecem, dando origem a fases altamente organizadas, com simetrias hexagonais 2D de DNA entre as lamelas. A incorporação completa de nucleotídeos é observada apenas quando grandes quantidades de DNA estão presentes. Esse fato aponta para importância maior de interações de volume excluído. Uma análise do parâmetro de Caillé mostra que as flutuações das membranas diminuem com a inserção de DNA. A partir dessas observações,é sugerido que a alteração das interações entre membranas, aliada à aparição de efeitos interfaciais entre DNA e membranas, é um mecanismo relevante no comportamento de fase. As propriedades dinâmicas dos nucleotídeos são investigadas através da técnica de FRAP (fluorescence recovery after photobleaching). Um modelo recentemente desenvolvido para análise de difusão anisotrópica é testado com sucesso, demonstrando estreita correlação entre estrutura e dinâmica. / An experimental study on the structural and dynamical properties of a hydrated DNA zwitterionic lipids complex is presented. By varying the water amount, it is possible to control the connement imposed by this host matrix over the organization of the nucleotides inserted within the water layers. The supramolecular assembly is investigated by X-rays diraction and techniques involving both optical and electron microscopy. A rich polymorphism of mesophases is observed as a function of connement. In the more hydrated regime, the fragments are distributed according to nematic orientation in-between lamellae. As the water amount decreases, the connement of bilayers over the particles increases and transmembrane correlations appear, giving raise to highly-ordered phases, with 2D-hexagonal symmetries of DNA embodied in the lamellar phase. The full incorporation of nucleotides by the lamellar phase is observed only in the presence of large amounts of DNA. This nding points to the major importance of excluded volume interactions. An analysis of the Caillé parameter shows that the insertion of DNA reduces the fluctuations of membranes. From these observations, it is suggested that changes in the interactions between bilayers, together with the appearance of interfacial eects between DNA and membranes, are a relevant mechanism for the phase behavior of these systems. The dynamical properties of nucleotides are investigated through the fluorescence recovery after photobleach (FRAP). A model recently developed for analyses of anisotropic difusion is sucessfully tested, demonstrating a close relationship between structure and dynamics.

Graphene, a single atomic layer of graphite, has many exciting electronic and mechanical properties. On a fundamental level, the quasi-relativistic behaviour of the charge carriers in graphene arises from the honeycomb-like atomic structure. Deforming the lattice changes the lengths of the carbon-carbon bonds, breaking the hopping symmetry between carbon sites. Mathematically, elastic strain in a graphene membrane can be described by additional terms in the low-energy effective Hamiltonian, analogous to the vector potential of an external magnetic field. Hence, certain non-uniform strain geometries produce so-called `pseudo-magnetic fields', leading to a predicted zero-field quantum Hall effect. These fictitious magnetic fields are distinct from an external magnetic field in that they are only observed by charge carriers within the membrane, and have opposing polarity for electrons in the K and K' valleys, preserving time-reversal symmetry of the lattice as a whole. Deforming graphene in the non-uniform manner required to produce a homogeneous pseudo-magnetic field has proven to be a huge technological challenge, however, restricting experimental evidence to scanning tunnelling spectroscopy measurements on, for example, highly deformed nanobubbles formed by the thermal expansion of an epitaxially grown sheet on a platinum substrate. These results stimulated a large amount of interest in strain-engineering electron transport in graphene, partly due to the extreme magnitude of the observed pseudo-magnetic field, a direct consequence of the strain components strongly varying over the space of a few nanometres, but the formation of nanobubbles is a highly stochastic process which cannot be reliably reproduced. Subsequent research found a way to fabricate nanobubbles with a high degree of consistency, but the measurements were still limited to local-probe techniques due to the nanoscale size of the devices. As such, a method to reliably induce a homogeneous pseudo-magnetic field within a micron-sized membrane would be an attractive proposition, and is the basis for the work presented within this thesis. The non-uniform strain required precludes a simple bending or elongation of the substrate, hence a more local method is required. A novel nanostructure consisting of suspended gold beams surrounding a graphene membrane will deform upon cooling to cryogenic temperatures, and crucially, the actuation mechanism can be designed to produce any configuration of strain, including uniaxial strain, triaxial strain and a fan-shaped deformation, the latter two of which are predicted to create homogeneous pseudo-magnetic fields within a membrane. Strain patterns which are predicted to produce experimentally significant pseudo-magnetic fields (~1 T) may be generated with complex actuation beams that are physically achievable. Furthermore, the actuation mechanisms may be utilised as electrical contacts to the membrane, allowing its conductivity to be measured in the context of a two- or multi-terminal measurement, in conjunction with an external magnetic field. The design of the devices was developed using finite-element analysis, and the behaviour verified by low-temperature imaging of prototypes. While, after careful annealing, some conventional two-terminal suspended devices exhibited quantum Hall features at very low fields, the fabricated strain-inducing devices did not display pseudo-Landau quantisation, nor Landau quantisation, due to the difficulties of using current annealing to clean devices post-fabrication. The presented work, however, could pave the way towards observing signatures of pseudo-magnetic fields in a range of experimental measurements, as well as creating alternative strain geometries.

Estudamos o comportamento crítico e transições de fase em modelos estocásticos irreversíveis, através de simulações numéricas, análise de campo médio e séries perturbativas. Na primeira parte do trabalho, analisamos o comportamento crítico de autômatos celulares irreversíveis, cujas regras dinâmicas são invariantes sob as operações de simetria do grupo C3v. Estudamos as transições de fase dinâmicas que ocorrem nos modelos e obtemos, através de simulações de Monte Carlo, expoentes críticos estáticos e dinâmicos. Nossos resultados indicam que os modelos pertencem a mesma classe de universalidade do modelo de Potts de três estados. Essa conjectura também foi desenvolvida considerando expansões análogas àquelas utilizadas na teoria de Landau de transições de fase. Na segunda parte do trabalho utilizamos o formalismo de operadores como uma forma ele abordar problemas de sistemas ele não-equilíbrio. Aplicamos o formalismo para construir séries perturbativas para modelos irreversíveis ele dois estados. / We study the critical behavior and phase transitions that take place in irreversible stochastic models through numerical simulations, mean field analysis and perturbative series. In the first part of this work we analyze the critical behavior of irreversible cellular automata whose dynamic rules are invariant under the symmetry operations of the point group C3v. We study the dynamical phase transitions that occur in the models and we obtain the static and dynamic critical exponents by the use of Monte Carlo simulations. Our results indicate that these models are in the same universality class as the three-state Potts model. This conjecture is also developed by considering expansions that are similar to those used in the Landau theory of phase transitions. In the second part of this work we use the operator fonnalism as a way to approach non- equilibrium systems. We apply this fonnalism in order to build perturbative series for two-state irreversible models.

Os ferrofluidos iônicos de \'MN\'\'FE IND. 2\'\'O IND. 4\', \'gama\' - \'FE IND. 2\'\'O IND. 3\' e \'CO\'\'FE IND. 2\'\'O IND. 4\' foram investigados pelas técnicas de óptica e espalhamento de raios X. Investigamos o comportamento desses ferrofluidos, na presença e na ausência de campo magnético e quando submetidos à variação de temperatura. A birrefringência óptica medida em função da temperatura, sem qualquer campo magnético, mostrou a existência de uma ordem tipo nemática nesses materiais. Os resultados obtidos com as medidas de anisotropia óptica podem ser explicados através da anisotropia de forma dos grãos e o fator clássico de despolarização da luz. Experimentos com a técnica de espalhamento de raios X mostrou a existência de pequenos agregados de grãos nas amostras estudadas. / Ionic ferrofluids of MnFe2O4, - Fe2Os Fe2Os and CoFe204 have been investigated by means of optical and x-ray- scattering techniques. An investigation on the behavior of such ferrofluids has been made, when in the presence and absence of a magnetic field, and when submitted to the variation of temperature. The optical birefringence measured as a function of temperature, without any magnetic field, showed the existence of a nematic-type order in these maaterials. The results obtained by the measured optical anisostropy could be explained by the shape anisostropy of the grains and the classical light depolarizing factors. X-ray scattering results indicate the existence of small aggregates in the samples studied.